Lessons from Math Class

For insight into the art of teaching as well as the use of technology in education, I’ve been diving into the dynamic microworld of the study of the use of curricular resources in mathematics (Fan, Trouche, Qi, Rezat & Visnovska, 2018). Theses researchers use video footage from classrooms to study in forensic detail what actually happens in a given lesson; they also create resource maps that speak to the sophisticated work of teaching, what Luc Trouche calls Documentational Genesis (Gueudet, Pepin & Trouche, 2012). Whether using a single textbook or cobbling together resources pulled from many sources, teachers inevitably interpret the intents and emphases of the original authors. Textbooks can be read as guides for teachers about how to teach, but from this perspective, seldom is adequate information included about the rationale for each choice, leaving teachers to connect the dots and fill in the blanks as best they can. Teachers, ultimately, have a lot of leeway as they implement textbook lessons.

Armed with powerful insights from such research, the question then becomes: how does one improve the quality of mathematics education? With better textbooks, yes, perhaps written with an awareness that teachers will inevitably change them during the delivery, perhaps by facilitating this process by making resources more malleable, or by including teachers in the process of creating and revising resources. Additionally, to improve educational systems, one needs to engage with teachers to deepen their understanding of what is intended, perhaps by exploring their Pedagogical Design Capacity (Remillard, Herbel-Eisenmann, & Lloyd, 2009) and by supporting their transition to ambitious teaching (Cortina & Visnovska in Fan et al, 2018).

Grounded in sociocultural perspectives, this vein of research highlights the key role of the teacher and looks at how they use their tools. It is fascinating to contrast the portraits of educators offered by the various researchers in France, South Africa, the United States, Mexico, Israel and China, what becomes evident is the diversity of school math cultures. While these intimate snippets from math classrooms around the world are not intended to be representative of each country (and they clearly reflect the varying research interests of the respective researchers), it is still striking to compare schools in France, where sophisticated teacher associations create, adapt, and share digital curricular resources within a dynamic, modern, and evolving system, with schools in South Africa or the United States where a less-plugged-in, more-isolated, less-resourced teacher follows, interprets, and deviates from a single textbook.

These insights from the world of school mathematics can also be extended to other subject areas, offering a deepened appreciation of what the work of teaching entails, examining closely the work of juggling curricular documents, ideas, and resources and bringing them, year after year, and lesson after lesson, to life for students. Cortina’s focus (in Fan et al, 2018) on facilitating teachers’ transition to ambitious teaching, and the monumental — and necessary — challenge of that undertaking, resonates with a need everywhere to invest in teachers as well as technology.

In my own role, working with instructional designers in higher education, these conversations echo a dynamic I see between heavy-handed designers of online courses who often conceive of a limited role for course instructors versus the many ways that course instructors, intentionally or not, reclaim didactic power during the implementation of courses, setting a tone that can sometimes be at odds with the course designer’s intent. More broadly, research into mathematics textbooks and their use speaks to something essential about the way we use tools (and technology), how they shape our tasks and how, at the same time, we take ownership of and in so doing shape the tools we use. Truly ambitious teaching embraces this fundamental aspect of critical thinking.